Operators on spaces of analytic functions
Studia Mathematica (1994)
- Volume: 108, Issue: 1, page 49-54
- ISSN: 0039-3223
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topSeddighi, K.. "Operators on spaces of analytic functions." Studia Mathematica 108.1 (1994): 49-54. <http://eudml.org/doc/216039>.
@article{Seddighi1994,
abstract = {Let $M_z$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_z$ is polynomially bounded if $∥M_p∥ ≤ C∥p∥_G$ for every polynomial p. We give necessary and sufficient conditions for $M_z$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.},
author = {Seddighi, K.},
journal = {Studia Mathematica},
keywords = {spaces of analytic functions; polynomially bounded; multipliers; spectral properties; cyclic subspace; operator of multiplication; finite-codimensional invariant subspaces},
language = {eng},
number = {1},
pages = {49-54},
title = {Operators on spaces of analytic functions},
url = {http://eudml.org/doc/216039},
volume = {108},
year = {1994},
}
TY - JOUR
AU - Seddighi, K.
TI - Operators on spaces of analytic functions
JO - Studia Mathematica
PY - 1994
VL - 108
IS - 1
SP - 49
EP - 54
AB - Let $M_z$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_z$ is polynomially bounded if $∥M_p∥ ≤ C∥p∥_G$ for every polynomial p. We give necessary and sufficient conditions for $M_z$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.
LA - eng
KW - spaces of analytic functions; polynomially bounded; multipliers; spectral properties; cyclic subspace; operator of multiplication; finite-codimensional invariant subspaces
UR - http://eudml.org/doc/216039
ER -
References
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- [6] H. Shapiro, Reproducing kernels and Beurling's theorem, Trans. Amer. Math. Soc. 110 (1964), 448-458. Zbl0147.11403
- [7] A. Shields and L. Wallen, The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788. Zbl0207.13801
- [8] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, 1976. Zbl0313.47029
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